6.6 Logarithmic equations (in class)

Solve the following equations. If you have two or more answers, write the smallest one.

(a) [math]\log_5(x^2-6x+9)=-2[/math]

(b) [math](\log_3x)^2-5\log_3x+6=0[/math]

(c) [math]\ln(x^2+3x-5)=\ln(2x^2-3)[/math]

(d) [math](\ln x)^2=\ln x^2[/math]

(e) [math]x^{1+\log_3x}=27x^3[/math]

Which of the following is the solution to the inequality [math]\log_{0.5}(2x+3)\geq2[/math]?

If [math]\log_x(x^2-12)-1\geq0[/math] when [math]x\geq a[/math] where [math]a[/math] is an integer, what is the value of [math]a[/math]?

If [math]x=\displaystyle{\frac{\ln a}{\ln b}}[/math] is the solution of the equation [math]3^{2x}\cdot4^{x-3}=9[/math] where [math]a[/math] and [math]b[/math] are integers and [math]b<10[/math], what is the value of [math]\dfrac{a}{b}[/math]?

Let [math]x[/math] and [math]y[/math] be nonzero real numbers. If [math]2\log_3(x-3y)=\log_3(2x)+\log_3(2y)[/math], find [math]\dfrac{x}{y}[/math].